A fast inverse Hankel Transform of first Order for computing vector-valued weight Functions appearing in Fundamental Measure Theory in cylindrical Coordinates

2020 ◽  
Vol 511 ◽  
pp. 112500
Author(s):  
Rolf Stierle ◽  
Joachim Gross
Keyword(s):  
Measure Theory ◽  
Hankel Transform ◽  
Weight Functions ◽  
Cylindrical Coordinates ◽  
First Order ◽  
Fundamental Measure Theory ◽  
Vector Valued

Strict Topologies for Vector-Valued Functions

1974 ◽  
Vol 26 (4) ◽  
pp. 841-853 ◽  
Author(s):  
Robert A. Fontenot
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Measure Theory ◽  
Strict Topology ◽  
Locally Compact ◽  
Topological Measure ◽  
Topological Measure Theory ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Compact Hausdorff Space

This paper is motivated by work in two fields, the theory of strict topologies and topological measure theory. In [1], R. C. Buck began the study of the strict topology for the algebra C*(S) of continuous, bounded real-valued functions on a locally compact Hausdorff space S and showed that the topological vector space C*(S) with the strict topology has many of the same topological vector space properties as C0(S), the sup norm algebra of continuous realvalued functions vanishing at infinity. Buck showed that as a class, the algebras C*(S) for S locally compact and C*(X), for X compact, were very much alike. Many papers on the strict topology for C*(S), where S is locally compact, followed Buck's; e.g., see [2; 3].

scholarly journals A fundamental measure theory for the sticky hard sphere fluid

2011 ◽  
Vol 134 (1) ◽  
pp. 014506 ◽  
Author(s):  
Hendrik Hansen-Goos ◽  
J. S. Wettlaufer
Keyword(s):  
Hard Sphere ◽  
Measure Theory ◽  
Hard Sphere Fluid ◽  
Fundamental Measure Theory

Systems Stability Using Weight Functions Method

2005 ◽  
Author(s):  
Ion Stroe ◽  
Dumitru I. Caruntu
Keyword(s):  
Classical Method ◽  
Liapunov Function ◽  
Weight Functions ◽  
Solution Stability ◽  
First Order ◽  
Controlled Systems ◽  
Linear And Nonlinear ◽  
Function Finding ◽  
Linear And Nonlinear Systems ◽  
First Order Differential Equations

A new method for systems stability analysis is presented. This method is called weight functions method and it replaces the problem of Liapunov function finding with a problem of finding a number of functions (weight functions) equal to the number of first order differential equations describing the system. It is known that there are not general methods for finding Liapunov functions. The weight functions method is simpler than the classical method since one function at a time has to found. This method’s conditions of solution stability for linear and nonlinear systems are presented. Applications such as Lurie-Postnikov problem and controlled systems stability are presented as well.

scholarly journals Generation results for vector-valued elliptic operators with unbounded coefficients in $$L^p$$ spaces

2021 ◽  
Author(s):  
Luciana Angiuli ◽  
Luca Lorenzi ◽  
Elisabetta M. Mangino ◽  
Abdelaziz Rhandi
Keyword(s):  
Lebesgue Space ◽  
Sufficient Conditions ◽  
Elliptic Operators ◽  
Unbounded Coefficients ◽  
First Order ◽  
Vector Valued

AbstractWe consider a class of vector-valued elliptic operators with unbounded coefficients, coupled up to the first order, in the Lebesgue space $$L^p({\mathbb {R}}^d;{\mathbb {R}}^m)$$ L p ( R d ; R m ) with $$p \in (1,\infty )$$ p ∈ ( 1 , ∞ ) . Sufficient conditions to prove generation results of an analytic $$C_0$$ C 0 -semigroup $${\varvec{T}}(t)$$ T ( t ) , together with a characterization of the domain of its generator, are given. Some results related to the hypercontractivity and the ultraboundedness of the semigroup are also established.

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